🧮 algebra

1. Problem: Given the vector \(\vec{a} = \begin{pmatrix} t \\ 8 \end{pmatrix}\), (a) Find the length \(|\vec{a}|\) when \(t=6\).

1. **Problem a:** Solve the equation $x(x - 4) = 0$. 2. The zero product property states that if $ab=0$, then either $a=0$ or $b=0$.

1. The problem involves understanding and plotting linear equations given in different forms, along with their corresponding points. 2. The general form of a linear equation is $y

1. **State the problem:** Simplify the expression $$\sqrt{\frac{25w^6}{x^2}} \div wx^3$$ leaving the answer with positive exponents. 2. **Rewrite the expression:** The division can

1. **State the problem:** We need to find the value of $y$ when $x=13$ for the function $$y=\frac{3}{2}\sqrt{x+3}.$$\n\n2. **Formula and explanation:** The function involves a squa

1. **Problem (a):** Express $\sqrt{50} - \frac{2}{\sqrt{8}}$ in the form $a\sqrt{b}$, where $a$ and $b$ are rational numbers. 2. **Step 1:** Simplify each term separately.

1. Das Problem lautet: Dividiere die Potenz $3^a$ durch $6 \cdot 2^a \cdot 5$.\n\n2. Die allgemeine Regel für Division von Potenzen mit gleicher Basis ist: $$\frac{x^m}{x^n} = x^{m

1. Planteamos el sistema para \(\lambda = 1\) usando la matriz \(A - \lambda I\): $$A - I = \begin{pmatrix} 1-1 & 2 & 3 \\ 0 & 0-1 & 2 \\ 0 & 1 & 1-1 \end{pmatrix} = \begin{pmatrix

1. **State the problem:** Simplify the expression $$\frac{27}{(-2)^5} \cdot \frac{4^8}{6^4}$$. 2. **Recall the rules:**

1. **State the problem:** Simplify the expression $$\frac{\sqrt{x^2 y z^3}}{\sqrt{x^2 y z^2}}$$ assuming $x, y, z > 0$. 2. **Use the property of square roots:** $$\frac{\sqrt{A}}{\

1. Das Problem ist: "Löse das bitte". Da keine spezifische Gleichung oder Aufgabe gegeben ist, kann ich nur allgemeine Schritte zum Lösen von Gleichungen erklären. 2. Allgemeine Fo

1. The problem is to determine which number or expression is greater between two given values. 2. To compare two numbers or expressions, we can subtract one from the other and anal

1. Problem: Berechne den Wert der Unbekannten in der Gleichung $10 - a = 4$. 2. Formel und Regeln: Um $a$ zu finden, isolieren wir $a$ auf einer Seite der Gleichung. Wir subtrahier

1. Problem statement: Simplify the expression $$-3 - [4x + 7x - (12 + 2x) + 4]$$ for $$x = -2$$. 2. Combine like terms inside the brackets:

1. Problem: Löse die Gleichung a) $7 \cdot 5^x = 9 - 6 \cdot 5^x$. 2. Wir wollen $x$ finden, das die Gleichung erfüllt.

1. **State the problem:** Factorise the expression $6x - 4$. 2. **Recall the factoring rule:** To factorise an expression, find the greatest common factor (GCF) of all terms.

1. **State the problem:** Fully factorise the expression $8p + 12$. 2. **Identify the common factor:** Both terms $8p$ and $12$ have a common factor of $4$.

1. **State the problem:** Solve the equation $$9^{3x - 7} = 81^{x + 2}$$. 2. **Rewrite bases as powers of the same base:**

1. **State the problem:** Solve the exponential equation $$2e^{5x} = 868$$ by taking the natural logarithm on both sides. 2. **Isolate the exponential term:** Divide both sides by

1. **State the problem:** Calculate the gross pay for the week given hourly wage, hours worked, and tips. 2. **Formula:** Gross pay = (hourly wage × hours worked) + (percentage of

1. **State the problem:** Calculate the gross pay for the week if you are paid 16.50 per hour and work the following hours: - Monday: 5:00 PM to 10:00 PM